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Klein’s Erlangen Program and Physical Geometry in the Early Twentieth CenturyThis paper notes that Klein’s Erlangen program for geometry did not constitute but laid out signposts for future research in group theory. Klein’s group-theoretic approach was central to Poincare’s geometric conventionalism which was based Klein’s tolerance about what transformation groups and generators may define a geometry. Extending Poincare’s work in the context of general relativity, Weyl’s innovation was to show that even the most general Riemannian geometries can be given a Klein-type group-theoretic definition by focusing on infinitesimal operators and generating elements. What deserves analysis is why both these exceptions arise when geometry is thought of in physical terms.
University of Texas at Austin